Title:	Multivariate Difference Between Two Groups
Version:	1.0.0
Description:	Estimation of multivariate differences between two groups (e.g., multivariate sex differences) with regularized regression methods and predictive approach. See Lönnqvist & Ilmarinen (2021) <doi:10.1007/s11109-021-09681-2> and Ilmarinen et al. (2023) <doi:10.1177/08902070221088155>. Includes tools that help in understanding difference score reliability, predictions of difference score variables, conditional intra-class correlations, and heterogeneity of variance estimates. Package development was supported by the Academy of Finland research grant 338891.
License:	GPL-3
Encoding:	UTF-8
BugReports:	https://github.com/vjilmari/multid/issues
RoxygenNote:	7.2.3
Imports:	dplyr (≥ 1.0.7), glmnet (≥ 4.1.2), stats (≥ 4.0.2), pROC (≥ 1.18.0), lavaan (≥ 0.6.9), emmeans (≥ 1.6.3), lme4 (≥ 1.1.27.1), quantreg (≥ 5.88), lmerTest (≥ 3.1.3), ggpubr (≥ 0.6.0), ggplot2 (≥ 3.4.4)
Suggests:	knitr (≥ 1.39), rmarkdown (≥ 2.14), overlapping (≥ 1.7), rio (≥ 0.5.29)
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2024-02-15 12:10:13 UTC; vjilm
Author:	Ville-Juhani Ilmarinen [aut, cre]
Maintainer:	Ville-Juhani Ilmarinen <vj.ilmarinen@gmail.com>
Repository:	CRAN
Date/Publication:	2024-02-15 13:20:02 UTC

Multivariate group difference estimation with regularized binomial regression

Description

Multivariate group difference estimation with regularized binomial regression

Usage

D_regularized(
  data,
  mv.vars,
  group.var,
  group.values,
  alpha = 0.5,
  nfolds = 10,
  s = "lambda.min",
  type.measure = "deviance",
  rename.output = TRUE,
  out = FALSE,
  size = NULL,
  fold = FALSE,
  fold.var = NULL,
  pcc = FALSE,
  auc = FALSE,
  pred.prob = FALSE,
  prob.cutoffs = seq(0, 1, 0.2),
  append.data = FALSE
)

Arguments

Details

fold = TRUE will apply manually defined data folds (supplied with fold.var) for regularization and obtain estimates for each separately. This can be a good solution, for example, when the data are clustered within countries. In such case, the cross-validation procedure is applied across countries.

out = TRUE will use separate data partition for regularization and estimation. That is, the first cross-validation procedure is applied within the regularization set and the weights obtained are then used in the estimation data partition. The size of regularization set is defined with size. When used with fold = TRUE, size means size within a fold."

For more details on these options, please refer to the vignette and README of the multid package.

Value

References

Lönnqvist, J. E., & Ilmarinen, V. J. (2021). Using a continuous measure of genderedness to assess sex differences in the attitudes of the political elite. Political Behavior, 43, 1779–1800. doi:10.1007/s11109-021-09681-2

Ilmarinen, V. J., Vainikainen, M. P., & Lönnqvist, J. E. (2023). Is there a g-factor of genderedness? Using a continuous measure of genderedness to assess sex differences in personality, values, cognitive ability, school grades, and educational track. European Journal of Personality, 37, 313-337. doi:10.1177/08902070221088155

See Also

cv.glmnet

Examples

D_regularized(
  data = iris[iris$Species == "setosa" | iris$Species == "versicolor", ],
  mv.vars = c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width"),
  group.var = "Species", group.values = c("setosa", "versicolor")
)$D

# out-of-bag predictions
D_regularized(
  data = iris[iris$Species == "setosa" | iris$Species == "versicolor", ],
  mv.vars = c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width"),
  group.var = "Species", group.values = c("setosa", "versicolor"),
  out = TRUE, size = 15, pcc = TRUE, auc = TRUE
)$D

# separate sample folds
# generate data for 10 groups
set.seed(34246)
n1 <- 100
n2 <- 10
d <-
  data.frame(
    sex = sample(c("male", "female"), n1 * n2, replace = TRUE),
    fold = sample(x = LETTERS[1:n2], size = n1 * n2, replace = TRUE),
    x1 = rnorm(n1 * n2),
    x2 = rnorm(n1 * n2),
    x3 = rnorm(n1 * n2)
  )

# Fit and predict with same data
D_regularized(
  data = d,
  mv.vars = c("x1", "x2", "x3"),
  group.var = "sex",
  group.values = c("female", "male"),
  fold.var = "fold",
  fold = TRUE,
  rename.output = TRUE
)$D

# Out-of-bag data for each fold
D_regularized(
  data = d,
  mv.vars = c("x1", "x2", "x3"),
  group.var = "sex",
  group.values = c("female", "male"),
  fold.var = "fold",
  size = 17,
  out = TRUE,
  fold = TRUE,
  rename.output = TRUE
)$D

Coefficient of variance variation

Description

Calculates three different indices for variation between two or more variance estimates. VR = Variance ratio between the largest and the smallest variance. CVV = Coefficient of variance variation (Box, 1954). SVH = Standardized variance heterogeneity (Ruscio & Roche, 2012).

Usage

cvv(data)

Arguments

Value

A vector including VR, CVV, and SVH.

References

Box, G. E. P. (1954). Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification. The Annals of Mathematical Statistics, 25(2), 290–302.

Ruscio, J., & Roche, B. (2012). Variance Heterogeneity in Published Psychological Research: A Review and a New Index. Methodology, 8(1), 1–11. https://doi.org/10.1027/1614-2241/a000034

Examples

d <- list(
  X1 = rnorm(10, sd = 10),
  X2 = rnorm(100, sd = 7.34),
  X3 = rnorm(1000, sd = 6.02),
  X4 = rnorm(100, sd = 5.17),
  X5 = rnorm(10, sd = 4.56)
)
cvv(d)

Coefficient of variance variation from manual input sample sizes and variance estimates

Description

Calculates three different indices for variation between two or more variance estimates. VR = Variance ratio between the largest and the smallest variance. CVV = Coefficient of variance variation (Box, 1954). SVH = Standardized variance heterogeneity (Ruscio & Roche, 2012).

Usage

cvv_manual(sample_sizes, variances)

Arguments

Value

A vector including VR, CVV, and SVH.

References

Box, G. E. P. (1954). Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification. The Annals of Mathematical Statistics, 25(2), 290–302.

Ruscio, J., & Roche, B. (2012). Variance Heterogeneity in Published Psychological Research: A Review and a New Index. Methodology, 8(1), 1–11. https://doi.org/10.1027/1614-2241/a000034

Examples

cvv_manual(sample_sizes=c(10,100,1000,75,3),
variances=c(1.5,2,2.5,3,3.5))

Standardized mean difference with pooled standard deviation

Description

Standardized mean difference with pooled standard deviation

Usage

d_pooled_sd(
  data,
  var,
  group.var,
  group.values,
  rename.output = TRUE,
  infer = FALSE
)

Arguments

Value

Descriptive statistics and mean differences

Examples

d_pooled_sd(iris[iris$Species == "setosa" | iris$Species == "versicolor", ],
  var = "Petal.Length", group.var = "Species",
  group.values = c("setosa", "versicolor"), infer = TRUE
)

Deconstructing difference score correlation with multi-level modeling

Description

Deconstructs a bivariate association between x and a difference score y1-y2 with multi-level modeling approach. Within each upper-level unit (lvl2_unit) there can be multiple observations of y1 and y2. Can be used for either pre-fitted lmer-models or to long format data. A difference score correlation is indicative that slopes for y1 as function of x and y2 as function of x are non-parallel. Deconstructing the bivariate association to these slopes allows for understanding the pattern and magnitude of this non-parallelism.

Usage

ddsc_ml(
  model = NULL,
  data = NULL,
  predictor,
  moderator,
  moderator_values,
  DV = NULL,
  lvl2_unit = NULL,
  re_cov_test = FALSE,
  var_boot_test = FALSE,
  boot_slopes = FALSE,
  nsim = NULL,
  level = 0.95,
  seed = NULL,
  covariates = NULL,
  scaling_sd = "observed"
)

Arguments

Value

Examples

## Not run: 
set.seed(95332)
n1 <- 10 # groups
n2 <- 10 # observations per group
dat <- data.frame(
  group = rep(c(LETTERS[1:n1]), each = n2),
  w = sample(c(-0.5, 0.5), n1 * n2, replace = TRUE),
  x = rep(sample(1:5, n1, replace = TRUE), each = n2),
  y = sample(1:5, n1 * n2, replace = TRUE)
)
library(lmerTest)
fit <- lmerTest::lmer(y ~ x * w + (w | group),
                      data = dat
)
round(ddsc_ml(model=fit,
              predictor="x",
              moderator="w",
              moderator_values=c(0.5,-0.5))$results,3)

round(ddsc_ml(data=dat,
              DV="y",
              lvl2_unit="group",
              predictor="x",
              moderator="w",
              moderator_values=c(0.5,-0.5))$results,3)


## End(Not run)

Deconstructing difference score correlation with structural equation modeling

Description

Deconstructs a bivariate association between x and a difference score y1-y2 with SEM. A difference score correlation is indicative that slopes for y1 as function of x and y2 as function of x are non-parallel. Deconstructing the bivariate association to these slopes allows for understanding the pattern and magnitude of this non-parallelism.

Usage

ddsc_sem(
  data,
  x,
  y1,
  y2,
  center_yvars = FALSE,
  covariates = NULL,
  estimator = "ML",
  level = 0.95,
  sampling.weights = NULL,
  q_sesoi = 0,
  min_cross_over_point_location = 0,
  boot_ci = FALSE,
  boot_n = 5000,
  boot_ci_type = "perc"
)

Arguments

Value

References

Edwards, J. R. (1995). Alternatives to Difference Scores as Dependent Variables in the Study of Congruence in Organizational Research. Organizational Behavior and Human Decision Processes, 64(3), 307–324.

Lakens, D., Scheel, A. M., & Isager, P. M. (2018). Equivalence Testing for Psychological Research: A Tutorial. Advances in Methods and Practices in Psychological Science, 1(2), 259–269. https://doi.org/10.1177/2515245918770963

Examples

## Not run: 
set.seed(342356)
d <- data.frame(
  y1 = rnorm(50),
  y2 = rnorm(50),
  x = rnorm(50)
)
ddsc_sem(
  data = d, y1 = "y1", y2 = "y2",
  x = "x",
  q_sesoi = 0.20,
  min_cross_over_point_location = 1
)$results

## End(Not run)

Difference between two dependent Pearson's correlations (with common index)

Description

Calculates Cohen's q effect size statistic for difference between two correlations, r_yx1 and r_yx2. Tests if Cohen's q is different from zero while accounting for dependency between the two correlations.

Usage

diff_two_dep_cors(data, y, x1, x2, level = 0.95, missing = "default")

Arguments

Value

Parameter estimates from the fitted structural path model.

Examples

set.seed(3864)
d<-data.frame(y=rnorm(100),x=rnorm(100))
d$x1<-d$x+rnorm(100)
d$x2<-d$x+rnorm(100)
diff_two_dep_cors(data=d,y="y",x1="x1",x2="x2")

Predicting algebraic difference scores in multilevel model

Description

Decomposes difference score predictions to predictions of difference score components by probing simple effects at the levels of the binary moderator.

Usage

ml_dadas(
  model,
  predictor,
  diff_var,
  diff_var_values,
  scaled_estimates = FALSE,
  re_cov_test = FALSE,
  var_boot_test = FALSE,
  nsim = NULL,
  level = 0.95,
  seed = NULL,
  abs_diff_test = 0
)

Arguments

Value

Examples

## Not run: 
set.seed(95332)
n1 <- 10 # groups
n2 <- 10 # observations per group

dat <- data.frame(
  group = rep(c(LETTERS[1:n1]), each = n2),
  w = sample(c(-0.5, 0.5), n1 * n2, replace = TRUE),
  x = rep(sample(1:5, n1, replace = TRUE), each = n2),
  y = sample(1:5, n1 * n2, replace = TRUE)
)
library(lmerTest)
fit <- lmerTest::lmer(y ~ x * w + (w | group),
  data = dat
)

round(ml_dadas(fit,
  predictor = "x",
  diff_var = "w",
  diff_var_values = c(0.5, -0.5)
)$dadas, 3)

## End(Not run)

Returns probabilities of correct classification for both groups in independent data partition.

Description

Returns probabilities of correct classification for both groups in independent data partition.

Usage

pcc(data, pred.var, group.var, group.values)

Arguments

Value

Vector of length 2. Probabilities of correct classification.

Examples

D_out <- D_regularized(
  data = iris[iris$Species == "versicolor" | iris$Species == "virginica", ],
  mv.vars = c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width"),
  group.var = "Species", group.values = c("versicolor", "virginica"),
  out = TRUE,
  size = 15
)

pcc(
  data = D_out$pred.dat,
  pred.var = "pred",
  group.var = "group",
  group.values = c("versicolor", "virginica")
)

Plot deconstructed difference score correlation

Description

Plots the slopes for y1 and y2 by x, and a slope for y1-y2 by x for comparison.

Usage

plot_ddsc(
  ddsc_object,
  diff_color = "black",
  y1_color = "turquoise",
  y2_color = "orange",
  x_label = NULL,
  y_labels = NULL,
  densities = TRUE,
  point_alpha = 0.5,
  dens_alpha = 0.75,
  col_widths = c(3, 1),
  row_heights = c(2, 1, 0.5),
  coef_locations = c(0/3, 1/3, 2/3),
  coef_names = c("b_11", "b_21", "r_x_y1-y2")
)

Arguments

Examples

set.seed(342356)
d <- data.frame(
  y1 = rnorm(50),
  y2 = rnorm(50),
  x = rnorm(50)
)
fit<-ddsc_sem(
  data = d, y1 = "y1", y2 = "y2",
  x = "x"
)

plot_ddsc(fit,x_label = "X",
          y_labels=c("Y1","Y2"))

Quantile correlation coefficient

Description

For computation of tail dependence as correlations estimated at different variable quantiles (Choi & Shin, 2022; Lee et al., 2022) summarized across two quantile regression models where x and y switch roles as independent/dependent variables.

Usage

qcc(
  x,
  y,
  tau = c(0.1, 0.5, 0.9),
  data,
  method = "br",
  boot_n = NULL,
  ci_level = 0.95
)

Arguments

Value

References

Choi, J.-E., & Shin, D. W. (2022). Quantile correlation coefficient: A new tail dependence measure. Statistical Papers, 63(4), 1075–1104. https://doi.org/10.1007/s00362-021-01268-7

Lee, J. A., Bardi, A., Gerrans, P., Sneddon, J., van Herk, H., Evers, U., & Schwartz, S. (2022). Are value–behavior relations stronger than previously thought? It depends on value importance. European Journal of Personality, 36(2), 133–148. https://doi.org/10.1177/08902070211002965

Examples

set.seed(2321)
d <- data.frame(x = rnorm(2000))
d$y <- 0.10 * d$x + (0.20) * d$x^2 + 0.40 * d$x^3 + (-0.20) * d$x^4 + rnorm(2000)
qcc_boot <- qcc(x = "x", y = "y", data = d, tau = 1:9 / 10, boot_n = 50)
qcc_boot$rho_tau

Reliability calculation for difference score variable that is a difference between two mean variables calculated over upper-level units (e.g., sex differences across countries)

Description

Calculates reliability of difference score (Johns, 1981) based on two separate ICC2 values (Bliese, 2000), standard deviations of mean values over upper-level units, and correlations between the mean values across upper-level units.

Usage

reliability_dms(
  model = NULL,
  data = NULL,
  diff_var,
  diff_var_values,
  var,
  group_var
)

Arguments

Value

A vector including ICC2s (r11 and r22), SDs (sd1, sd2, and sd_d12), means (m1, m2, and m_d12), correlation between means (r12), and reliability of the mean difference variable.

References

Bliese, P. D. (2000). Within-group agreement, non-independence, and reliability: Implications for data aggregation and analysis. In K. J. Klein & S. W. J. Kozlowski (Eds.), Multilevel theory, research, and methods in organizations: Foundations, extensions, and new directions (pp. 349–381). Jossey-Bass.

Johns, G. (1981). Difference score measures of organizational behavior variables: A critique. Organizational Behavior and Human Performance, 27(3), 443–463. https://doi.org/10.1016/0030-5073(81)90033-7

Examples

set.seed(4317)
n2 <- 20
n1 <- 200
ri <- rnorm(n2, m = 0.5, sd = 0.2)
rs <- 0.5 * ri + rnorm(n2, m = 0.3, sd = 0.15)
d.list <- list()
for (i in 1:n2) {
  x <- rep(c(-0.5, 0.5), each = n1 / 2)
  y <- ri[i] + rs[i] * x + rnorm(n1)
  d.list[[i]] <- cbind(x, y, i)
}

d <- data.frame(do.call(rbind, d.list))
names(d) <- c("x", "y", "cntry")
reliability_dms(
  data = d, diff_var = "x",
  diff_var_values = c(-0.5, 0.5), var = "y", group_var = "cntry"
)

Predicting algebraic difference scores in structural equation model

Description

Predicting algebraic difference scores in structural equation model

Usage

sem_dadas(
  data,
  var1,
  var2,
  center = FALSE,
  scale = FALSE,
  predictor,
  covariates = NULL,
  estimator = "MLR",
  level = 0.95,
  sampling.weights = NULL,
  abs_coef_diff_test = 0
)

Arguments

Value

References

Edwards, J. R. (1995). Alternatives to Difference Scores as Dependent Variables in the Study of Congruence in Organizational Research. Organizational Behavior and Human Decision Processes, 64(3), 307–324.

Examples

## Not run: 
set.seed(342356)
d <- data.frame(
  var1 = rnorm(50),
  var2 = rnorm(50),
  x = rnorm(50)
)
sem_dadas(
  data = d, var1 = "var1", var2 = "var2",
  predictor = "x", center = TRUE, scale = TRUE,
  abs_coef_diff_test = 0.20
)$results

## End(Not run)

Testing and quantifying how much ipsatization (profile centering) influence associations between value and a correlate

Description

Testing and quantifying how much ipsatization (profile centering) influence associations between value and a correlate

Usage

value_correlation(
  data,
  rv,
  cf,
  correlate,
  scale_by_rv = FALSE,
  standardize_correlate = FALSE,
  estimator = "ML",
  level = 0.95,
  sampling.weights = NULL,
  sesoi = 0
)

Arguments

Value

Examples

## Not run: 
set.seed(342356)
d <- data.frame(
 rv1 = rnorm(50),
 rv2 = rnorm(50),
 rv3 = rnorm(50),
 rv4 = rnorm(50),
 x = rnorm(50)
)
d$cf<-rowMeans(d[,c("rv1","rv2","rv3","rv4")])
fit<-value_correlation(
 data = d, rv = c("rv1","rv2","rv3","rv4"), cf = "cf",
 correlate = "x",scale_by_rv = TRUE,
 standardize_correlate = TRUE,
 sesoi = 0.10
)
round(fit$variability_summary,3)
round(fit$association_summary,3)

## End(Not run)

Variance partition coefficient calculated at different level-1 values

Description

Calculates variance estimates (level-2 Intercept variance) and variance partition coefficients (i.e., intra-class correlation) at selected values of predictor values in two-level linear models with random effects (intercept, slope, and their covariation).

Usage

vpc_at(model, lvl1.var, lvl1.values)

Arguments

Value

Data frame of level 2 variance and std.dev. estimates at level 1 variable values, respective VPCs (ICC1s) and group-mean reliabilities (ICC2s) (Bliese, 2000).

References

Goldstein, H., Browne, W., & Rasbash, J. (2002). Partitioning Variation in Multilevel Models. Understanding Statistics, 1(4), 223–231. https://doi.org/10.1207/S15328031US0104_02

Bliese, P. D. (2000). Within-group agreement, non-independence, and reliability: Implications for data aggregation and analysis. In K. J. Klein & S. W. J. Kozlowski (Eds.), Multilevel theory, research, and methods in organizations: Foundations, extensions, and new directions (pp. 349–381). Jossey-Bass.

Examples

fit <- lme4::lmer(Sepal.Length ~ Petal.Length +
  (Petal.Length | Species),
data = iris
)

lvl1.values <-
  c(
    mean(iris$Petal.Length) - stats::sd(iris$Petal.Length),
    mean(iris$Petal.Length),
    mean(iris$Petal.Length) + stats::sd(iris$Petal.Length)
  )

vpc_at(
  model = fit,
  lvl1.var = "Petal.Length",
  lvl1.values = lvl1.values
)